Squares and Square Roots

- If a natural number
*m*can be expressed as*n*^{2}, where*n*is also a natural number, then*m*is a square number. The square numbers are also called**perfect squares.**

Examples: 1, 4, 9, 16, 25, 36 … are perfect squares.

**Prime factorization method of finding the square roots of numbers**

The square root of 67600 can be found by prime factorization method as follows:

The number 67600 can be prime factorized as:

__2 × 2__ × __2 × 2__ × __5 × 5__ × __13 × 13__

The numbers, 2, 2, 5, 13, occur in pairs. Therefore,

**Example: **Find the smallest number by which 252 can be multiplied to make it a perfect square.

**Solution: **We have, 252 = __2 × 2__ × __3 × 3__ × 7

The number 7 does not occur in pair. Therefore, if we multiply 252 by…

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